(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Inside the sphere x^{2}+ y^{2}+ z^{2}= R^{2}and between the planes z = [tex]\frac{R}{2}[/tex] and z = R. Show in cylindrical and spherical coordinates.

2. Relevant equations

[tex]\iiint\limits_Gr\,dz\,dr\,d\theta[/tex]

[tex]\iiint\limits_G\rho^{2}sin\,\theta\,d\rho\,d\phi\,d\theta[/tex]

3. The attempt at a solution

[tex]2\int_0^{2\pi}\int_0^{R\sqrt{\frac{3}{4}}}\int_?^{\sqrt{R^{2}-r^{2}}}r\,dz\,dr\,d\theta[/tex]

Is my upper limit for r correct? How do I find the lower limit for z?

[tex]\int_0^{2\pi}\int_0^{\frac{\pi}{3}}\int_?^R\rho^{2}sin\,\theta\,d\rho\,d\phi\,d\theta[/tex]

How do I find the lower limit for rho?

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# Setting up a triple integral using cylindrical & spherical coordinates

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